Decimals are a way to write numbers that are not full numbers.
A full number is like 1, 2, 3, 4, 5… without any extra parts.
But sometimes, we need to show a part of something, and decimals help with that.
Example: If you have 1 chocolate and your friend gives you half of another chocolate, you don’t have 1 chocolate β you have 1.5 chocolates.
Here, 0.5 shows the half.
Why Do We Need Decimals?
We need decimals because not everything in life is a full number.
Fractions can also show parts (like 1/2), but decimals are easier to read and use in calculations.
Reasons we need decimals:
To show parts of something β like money, length, weight, time.
To be more accurate β measuring things precisely.
To make math easier β decimals are easier to add, subtract, multiply, and divide compared to fractions in many cases.
Example:
A packet of chips that weighs 1 and a half kilograms can be written as 1.5 kg.
If a movie lasts 2 hours and 15 minutes, in decimal form it’s about 2.25 hours.
Where Do We See Decimals in Daily Life?
Decimals are everywhere!
Here are some examples:
Money β If something costs βΉ10.50, the “.50” means 50 paise.
Length β Your height could be 1.62 meters.
Weight β A watermelon might weigh 2.75 kg.
Sports β Long jump distances like 6.85 meters.
Science β Temperature like 36.6Β°C.
Fun fact: Without decimals, we would need to write everything as fractions, which can be confusing in real life.
Understanding the Decimal Point
The decimal point is the dot in a decimal number.
It separates the full number from the part.
Example: In 12.34
12 is the whole number part.|
34 is the decimal part (34 hundredths).
Think of the decimal point like a wall:
Left side = whole numbers (ones, tens, hundreds…).
Right side = parts of a whole (tenths, hundredths, thousandths…).
Place Value in Decimals
Just like whole numbers have place values (ones, tens, hundreds…), decimals have place values after the decimal point.
Place Value Name | Example
Tenths (1/10) | 0.1 = one-tenth
Hundredths (1/100) | 0.01 = one-hundredth
Thousandths (1/1000) | 0.001 = one-thousandth
Example: 45.678
45 is the whole number part.
6 is in the tenths place (6/10).
7 is in the hundredths place (7/100).
8 is in the thousandths place (8/1000).
Decimals and Fractions β The Connection
Decimals and fractions are two different ways to show the same thing.
Examples:
– 0.5 = 5/10 = 1/2
– 0.25 = 25/100 = 1/4
– 0.75 = 75/100 = 3/4
This means if you understand fractions, decimals become easy.
Decimals just replace the “/” with a dot and a place value.
Comparing Decimals
To compare decimals:
Look at the whole number part first.
If they are the same, compare the tenths, then hundredths, and so on.
Example:
– 3.45 vs 3.56 β Both have “3” as the whole number.
But in tenths, 4 < 5, so 3.45 < 3.56.
Tip: Always compare digit by digit.
Adding and Subtracting Decimals
When adding or subtracting:
Line up the decimal points.
Add or subtract normally.
Example:
12.45
+ 3.20
——–
15.65
Remember: If you don’t align decimal points, your answer will be wrong.
Multiplying and Dividing Decimals
Multiplication:
Multiply as if thereβs no decimal.
Count total decimal places in both numbers.
Put decimal in the result.
